4Th Place - Profesor František Vencovský Award 4. místo - Cena profesora Františka Vencovského Monetary Policy Stance and Future Inflation: The Case of Czech Republic Měnová politika a budoucí inflace: Evidence pro Českou republiku ROMAN HORVÁTH* 1 Introduction Inflation targeting regimes are increasingly popular around the world. For example, regarding the Central and Eastern Europe while the first two countries adopted explicit inflation targeting regime in 1998, there are already seven countries conducting inflation targeting in 2006 and others are contemplating to do so (International Monetary Fund, 2006).1 A characteristic feature of inflation targeting is that central banks set short-term nominal interest rate in the way to get inflation and output at their targeted levels. The level of interest rates that is associated with this objective is often labeled as policy neutral rate. In this regard, Woodford (2003) notes that central banks should on average track policy neutral rate to stabilize the economy. In a similar fashion, Taylor (1999) emphasizes that the measurement of policy neutral rate is one of key issues for countries targeting inflation. In this respect, it is of great importance for central banks to identify as precisely as possible the policy neutral rate.This is quite intricate exercise, as the policy neutral rate is unobservable; however its mis-measurement is high-priced, as it likely results in over- or undershooting the inflation target. In this light, it is quite striking that remarkably little evidence is available for Central and Eastern European Countries (CEECs) on the estimation of policy neutral rate. While there are dozens of studies on equilibrium exchange rates in the EU new members, there is surprisingly very little evidence on equilibrium interest rates (Brzoza-Brzezina, 2006, seem to the only exception with evidence on Poland). This imbalance is rather paradoxical, as half of EU new members target inflation (Czech Republic, Hungary, Poland, Romania and Slovakia), for which the concept as well as measurement of policy neutral rate is of primary importance for the conduct of monetary policy.2 Consequently, this paper tries to bridge this gap. * Czech National Bank and Institute of Economic Studies, Charles University (Prague). All remaining errors are entirely my own. The views expressed in this paper are not necessarily those of the Czech National Bank. 1 Czech Republic and Poland adopted inflation targeting in 1998, followed by Hungary in 2001, Romania and Slovakia in 2005 and Armenia and Serbia in 2006 (note this is an updated list of Table 1 in IMF, 2006). Ukraine is likely to adopt inflation targeting in near future (IMF, 2006). 2 See Coats et al. (2003) and Kotlan and Navrátil (2003) on Czech monetary policy. 080 ACTA VŠFS, 1/2008, roc. 2 This paper addresses the issue of policy neutral rate estimation in one of EU new member states, the Czech Republic, based on various specifications of simple Taylor-type monetary policy rules. Former transition country provides an interesting case to evaluate policy neutral interest rate, as one can expect certain pattern in the path of nominal and real equilibrium interest rates over longer time horizon (note that policy neutral rate is in fact short-term nominal equilibrium interest rate, more on definitions below). Lipschitz et al. (2006) points out that at the outset of transition the capital/labor ratios were much lower than those in Western Europe and therefore the marginal product of capital and for that reason real equilibrium interest rate was rather high. Given the capital accumulation over the course of transition, there should be tendency for the real equilibrium interest rate to decrease. From open economy perspective, EU new members exhibited a fall of exchange rate risk premium during their transition process to market economy (Benes and N'Diaye, 2004), which also puts a downward pressure on real equilibrium interest rates (Archibald and Hunter, 2001). Analogously, it is a well-documented empirical regularity that these countries exhibit real equilibrium exchange rate appreciation (see Egert et al., 2006 for a comprehensive survey of the sources of appreciation). A decrease in foreign equilibrium interest rate, which is reported by several authors for the euro area (e.g. Wintr et al., 2005), may, especially in small open economy, reduce the level of domestic equilibrium interest rate as well. Additionally, the path of nominal equilibrium interest rates should reflect not only the decrease of real equilibrium rates, but also successful disinflation in transition countries (see Korhonen and Wachtel, 2006). All in all, aforementioned arguments provide rationale to model policy neutral rate as time-varying. In this paper we provide first the estimation of monetary policy rules with time-varying intercept to assess the fluctuations of policy neutral interest rate over time.The novelty of our approach lies in estimation of policy neutral rate by the time-varying parameter model with endogenous regressors (Kim, 2006).3 Unlike'conventional'time-varying parameter model, this approach is robust to endogeneity of explanatory variables, which is indeed relevant when estimating the monetary policy rules. Additional feature of this paper is that we utilize ex-post as well as real-time based data (see e.g. Orphanides, 2001, on realtime data analysis within monetary policy rules framework), specifically the real-time output gap and real-time inflation forecast of Czech National Bank's (CNB) to estimate the monetary policy rules. One of our primary policy applications, except for measuring policy neutral rate by the novel technique, is also proposing a measure of monetary policy stance based on a deviation of actual interest rate from policy neutral rate. Anticipating our results, we find this measure of monetary policy stance quite useful in predicting both the level as well as change of future inflation rate. The paper is organized as follows. Section 2 discusses the related literature. Section 3 describes our data and empirical methodology. Section 4 gives the results on the estimation of time-varying estimates of policy neutral rate as well as analysis of ability of monetary 3 Note that in working paper version of Kim (2006), this procedure is also labeled as augmented Kaiman filter. ACTA VSFS, 1/2008, roc. 2 081 policy stance to predict future inflation developments. Section 5 concludes. Appendix with additional results follows. 2 Related Literature 2.1 Methodological Background It has been acknowledged in monetary economics for a long time that there exists some unobservable real interest rate that equilibrates aggregate demand and aggregate supply (Woodford, 2003). When actual real interest rate is equal to the unobservable, price stability is achieved. This unobservable rate is often labeled as natural rate of interest or equilibrium interest rate. Equivalently, it has been noted that equilibrium interest rate is the real interest rate that prevails, when prices are fully flexible in all markets (Neiss and Nelson, 2003; Woodford, 2003). Consequently, equilibrium interest rate or natural rate of interest is fairly general concept and in principle, it may be well associated both with short-term, medium-term or long-term interest rates. In this context, it is worth pointing out that the determinants of equilibrium interest rate are likely to differ according to time horizon (different frequency movements). In the long-term, the level of equilibrium interest rate is influenced by supply-side structural characteristics of economy such as long-run growth potential, which in turn depends on technological progress, population growth and inter-temporal substitution of consumption (Crespo-Cuaresma etal., 2005). In the medium-term, equilibrium interest rate is associated with business cycle. In the short-term, equilibrium interest rate is linked merely to demand factors related to monetary policy and its targeting horizon (Archibald and Hunter, 2001). Here monetary policy may systematically effect inflation expectations and in turn the level of short-term nominal equilibrium rate. For the purposes of monetary policy conduct, it is vital to know which level of interest rate monetary authority should set in order to achieve price stability (i.e. neutral policy stance). As the primary monetary policy instrument is the level of short-term interest rate, equilibrium interest rate in this context is rather short-term concept and is often labeled as policy neutral rate (Coats et al., 2003; Lam and Tkacz, 2004; Beneš et al., 2005). Policy neutral rate thus represents nominal equilibrium interest rate and is defined as real equilibrium interest rate plus expected inflation (Coats et al., 2003). In other words, policy neutral rate is linked to short-term nominal interest rate over which central bank has substantial control and thus, policy neutral rate may be understood as a bit narrower concept in comparison to equilibrium interest rate and natural rate of interest.4 Shall interest rate policy of monetary authority strictly follow the neutral rate, when targeting inflation? Not necessarily. First point is that obviously there is uncertainty in policy neutral rate measurement. Second, more importantly, there are shocks to which is sub-optimal for the authority to react. More specifically, central banks deliberately do not react 4 For convenience, we use policy neutral rate, natural rate of interest and equilibrium interest rate in the following text interchangeably to a certain extent. However, when we want to emphasize the short-run concept of it, we always use the term policy neutral rate. 082 ACTA VŠFS, 1/2008, roc. 2 to the first-round effects of cost-push shocks, as this can be destabilizing the economy in the short run. This may however alter inflation expectation of economic agents, if some fraction of them is myopic, and as a result, induce a change in policy neutral rate. In such case, central bank interest rate policy may temporarily deviate from policy neutral rate. 2.2 Methods for Natural Rate of Interest Estimation Generally, there are several main methods to estimate the natural rate of interest (see e.g. Giammarioli and Valla, 2004, for survey).5The simplest is to assume that the equilibrium is captured reasonably well by some univariate trend such as HP filter. Nevertheless, a number of papers document that the estimates based on these filters is often misleading (Clark and Kozicki, 2005). In general, the limitations of the univariate methods have been pointed out by many authors (e.g. Canova, 1998). Another method to derive equilibrium interest rates is based on the estimation of simple monetary policy rule of central bank (Taylor, 1993). The reaction function typically associates short-term interest rates to its lagged value, a difference between inflation (forecast) and its target, and output gap. The intercept of the estimated reaction function can be interpreted as the nominal equilibrium interest rate (this is, the interest rate that would prevail when inflation and output are at their targeted values). This method has been applied to estimate the equilibrium interest rates by e.g. Clarida et al. (1998, 2000) and Orphanides (2001) for the United States and Germany, Adam et al. (2005) for the United Kingdom and Gerdesmeier and Roffia (2004,2005) for the euro area. Nevertheless, the assumption of constant equilibrium interest rates is often found too restrictive over the longer-term horizon (for example, when there is a change in monetary policy strategy). Consequently, it is possible to model the equilibrium interest rate, or more generally monetary policy rule as time-varying (see Plantier and Scrimgeour, 2002, Elkhoury, 2006 and Kim and Nelson, 2006). Typically, these studies find rationale to model the rule as time-varying, given that the equilibrium interest rate sometimes fluctuates considerably over longer time horizons (as well as other parameters in policy rule). Generally, the monetary policy rules approach measures the behavior of central bankand assumes that central bank estimates equilibrium interest rates correctly. In case of central bank's systematic mis-measurement of equilibrium rates, it is likely that equilibrium rates retrieved from the estimation of reaction function are mis-measured as well. Structural time series models represent another common method to measure equilibrium interest rates as well. The primary contribution in this area is Laubach and Williams (2003), who formulate a simple empirical model containing IS curve, Phillips curve and an equation linking equilibrium interest rate to trend growth, and model equilibrium interest rates and potential output as unobserved components. Their method has gained popularity recently and has been applied by Manrique and Marques (2004) for the U.S. and Germany, Mesonnier 5 Note that we do not present the exhaustive list of methods for equilibrium interest rate estimation, e.g. Brzoza-Brzezina (2006) proposes structural vector autoregression model in this regard. In general, the role of equilibrium interest rate for monetary policy conduct is discussed extensively by Taylor (1993), Woodford (2003) orAmato (2005). ACTA VSFS, 1/2008, roc. 2 083 and Renne (2007) for the euro area and Wintr,Guarda and Rouabah (2005) for the euro area6 and Luxembourg as well. In principle, the joint estimation of equilibrium interest rates and output gap is an advantage of this approach; however it also reduces the degrees of freedom, which may be an issue for transition countries with rather short time series. Equilibrium interest rates can also be estimated within stochastic dynamic general equilibrium models. The advantage of this type of literature is that it specifies the structure of economy and thus in principle allows an identification of variety of shocks hitting the economy. On the other hand, Levin et al. (1999) find that more complex models seem to be less robust to model uncertainty (see also Giammarioli and Valla, 2004). Consequently, these model outcomes may be quite sensitive to model assumptions. The recent examples of this approach to estimate equilibrium interest rates include Giammarioli and Valla (2003), Neiss and Nelson (2003) and Smets and Wouters (2003). The last major stream of literature estimates equilibrium interest rates from the yield curve and asset pricing models. Bomfim (2001) uses inflation linked bonds in order to eliminate the distortions from inflation expectations and retrieves equilibrium interest rates from the realized yields on U.S. Treasury inflation-indexed securities. In this regard, Giammarioli and Valla (2004) discuss equilibrium interest rate estimates in relation to consumption capital asset pricing models. In general, this stream of literature hinges on a notion of liquid financial markets and thus this approach is viable especially for countries with developed financial markets. 3 Data and Empirical Methodology In this part, we discuss the methodology and dataset we employ to evaluate the policy neutral rate fluctuations in the Czech Republic. Concretely, we estimate a variety of backward or forward looking monetary policy rules with time-varying policy neutral rate. 3.1 Monetary Policy Rules A starting point for a formal derivation of monetary policy rule is a reasonable assumption that central banktargets to set nominal interest rate in line with the state of economy (see Clarida et al., 1998, 2000), as postulated in Eq. (1): rt denotes the targeted interest rate, ^ is the policy neutral rate, stands for the central bank forecast of yearly inflation rate i periods ahead, is the central bank's inflation target. xt represents a measure of output gap. E(.) is the expectation operator and Q, is the information set available at the time when interest rates are set. Hereinafter, we set i either equal to 12 months to reflect the CNB's actual targeting horizon7 or alternatively 6 See Crespo-Cuaresma et al. (2004) on related estimates on Euro area using somewhat different methodology. 7 This in line with the CNB main forecasting model - Quarterly Prediction Model; see Coats et al., 2003. The actual targeting horizon is 12-18 months, but due to data limitations we prefer to work with 12 months. In general, see Batini and Nelson, 1999, for contributions on optimal targeting horizon. Note also that policy (D ACTA VSFS, 1/2008, roc. 2 to 0, i.e. using the current inflation for sensitivity analysis. Therefore, Eq. (1) links targeted nominal interest rates to a constant (i.e. interest rate - policy neutral rate - that would prevail, when expected inflation is at the target and output gap is null), the deviation of expected inflation from the target and output gap. Nevertheless, Eq. (1) is often argued to be too restrictive, as it does not account for interest rate smoothing of central banks. Clarida et al. (1998) assume that central bank adjusts the interest rate sluggishly to the targeted value. This is so for a number of reasons. For example, Goodfriend (1991) puts forward the concerns over the stability of financial markets. Sack (1997) highlights uncertainty about the effects of interest rate changes on the economy.8 Instead of explicit listing of various factors behind the interest rate smoothing, Clarida et al. (1998) assume for simplicity that actual policy interest rate is a combination of its lagged value and the targeted policy rate as in Eq. (2). rt = Pr,-i +(1-P)r* + v, (2),9 where ps [0,l] . In line with Clarida etal. (1998), substituting Eq. (2) into Eq. (1) and eliminating unobserved forecast variables results in Eq. (3): rt = (l-p)r+ a{nt+i - nM)+ fix, + prt_x + e, (3) Note that disturbance term e, is a combination of forecast errors and is thus orthogonal to all information available in time t ( n,). Next, in order to estimate time-varying neutral policy rate we apply structural time-varying coefficient model with endogenous regressors. Kim (2006) shows that conventional time-varying parameter model delivers inconsistent estimates, when explanatory variables are correlated with the disturbance term, which is indeed relevant, when estimating policy rules. It is interesting to note that the correlation of and xt with £, in Eq. (3) is almost always taken into account in empirical work on time-invariant rules (as typically estimated by the GMM), while it is almost never considered in literature on time-varying monetary policy rules (Kim and Nelson, 2006, seem to be the exemption). So, Kim (2006) derives a consistent estimator of time-varying parameter model, when regressors are endogenous. In line with Kim (2006), we estimate the following empirical model: neutral rate is defined as the real rate plus the expected inflation in period t+k, where k is given by the maturity of interbank rate (in our case k=3). k is thus different from forecasting horizon i. As argued by Clarida et al. (2000), this is not very relevant in practice, as the short-term interbank interest rates at various maturities are strongly linked together. Indeed, the correlation of 3M PRIBOR and 12M PRIBOR - to reflect that /'= 12 - stands at 0.991 in our sample. 8 Nevertheless, Rudebusch (2006) recently questioned the extent of monetary policy inertia and argued that the inertia is rather low. 9 We have estimated the monetary policy rules including higher lags of interest rates, but failed to find it significant. ACTA VSFS, 1/2008, roc. 2 085 1 =(!-/>) r,+ a(nM-nM)+pxt + prM + e t (4) r, =r,-i+^, ~i.i.d.N(o,al) nM = + °9 w,_2, x,_ls x,_2, r,_, and r* (foreign interest rate - 1YEURIBOR). We assume that the parameters in the Eqs. (6) and (7) are time-invariant. Next, the correlation between the standardized residuals 1- > - rt r, + v V J 1 J Our estimation framework begins with the following regression: where ^t+i is yearly inflation ;' months ahead, where ;=12,....,24. Next, we control for the lagged inflation terms: n h=\ where for simplicity we set n=4.17 (9) 1 \ km = 00+01 \rt-r, r, vv J, ' J (10) Using Eqs. (9) and (10), we investigate the information content of monetary policy stance on the future level of inflation. We also re-specify the above equations to address the future change in the inflation rate as follows: (( _ > 1 > *m ~ n, = 00 + 01 \rt-r, r K\ J i j (f _ \ - 71, = 0 + 01 \rt-r, r k\ j 1 j +v, (11) (12) The results from Eq. (9) are given in Table A.3 in the Appendix. Our definition of monetary policy stance seems to be informative for future inflation, explaining typically about 1/3 of its variance. These results are largely confirmed, when controlling for the lagged inflation terms, as suggested the estimation of Eq. (10) presented in Table A.4. The results suggest that when actual interest rate is 10% above the policy neutral rate, inflation is likely to fall by about 1 p.p. at the monetary policy horizon. Similarly, policy neutral rate seems to be relatively good predictor of the future change of inflation rate, as presented in Table A.5. This result is largely robust to inclusion of lagged inflation as well (see Table A.6). All in all, the results suggest usefulness of policy neutral rate in understanding future behavior of inflation.18 5 Conclusions This paper analyzes the policy neutral rate in the Czech Republic. In order to do so, we estimate various specifications of simpleTaylor-type monetary policy rules at the monthly / 7 We also included higher lags, but with little impact on the results. 18 We also tested the robustness of our results by including other macroeconomic variables to Eqs. (10) and (12) such as real effective exchange rate, credit and monetary aggregates. The results remain largely unchanged and are available upon request. 094 ACTA VSFS, 1/2008, roc. 2 frequency from 2001:1 to 2006:9. To address the sensitivity of results, the specifications differ based on whether we include real-time or ex-post revised data, employ backward or forward-looking monetary policy rules or vary the measure of output gap. To estimate time-varying policy neutral rate, we use time-varying parameter model with endogenous regressors (Kim, 2006).This approach is especially appealing, when estimating monetary policy rules, as it addresses the endogeneity of inflation (forecast) and output gap. Indeed, the results support the usefulness of applying time-varying parameter model with endogenous regressors. The bias correction terms, accounting for the endogeneity of regressors, are typically significant, the log likelihood improves after their inclusion and the estimated path of policy neutral rate is for certain periods considerably different. The results indicate that policy neutral rate decreases gradually over the course of sample period from some 5% in 2001 to about 2.5% in 2006 showing a substantial interest rate convergence to the levels comparable to the euro area. Over the longer time horizon, the decrease may be supported a number of factors such as capital accumulation, the decrease in risk premium, real equilibrium exchange rate appreciation as well as successful disinflation of Czech economy and well-anchored inflation expectations. One of our primary policy applications, except for measuring policy neutral rate by the novel technique, is also proposing a measure of monetary policy stance based on a deviation of actual interest rate from policy neutral rate. Our results indicate that this measure is quite useful in predicting future inflation developments. More specifically, monetary policy stance affects both the level as well as change of future inflation rate. In terms of future research, it would be interesting to see more evidence on other inflation targeting countries to uncover, whether our proposed monetary policy stance measure remains useful predictor of future inflation developments, as we find in the case of Czech Republic. Abstract This paper examines time-varying policy neutral interest rate in real time for the Czech Republic in 2001:1-2006:09 estimating various specifications of simple Taylor-type monetary policy rules. For this reason, we apply a structural time-varying parameter model with endogenous regressors.The results indicate that policy neutral rate gradually decreased over sample period to the levels comparable to those of in the euro area. Next, we propose a measure of monetary policy stance based on a difference between the actual interest rate and estimated policy neutral rate and find it a useful predictor of the level as well as change of future inflation rate. Keywords policy neutral rate, Taylor rule, time-varying parameter model with endogenous regressors JEL classification / JEL klasifikace E43, E52, E58 ACTA VSFS, 1/2008, roc. 2 095 Souhrn Tento článek analyzuje politicky neutrální („rovnovážnou") úrokovou míru s tzv. daty v reálném čase v České republice od 2001:1 do 2006:09 na základě odhadů různých specifikací Taylorova pravidla. Aplikujeme strukturální model s časově proměnlivými parametry a s endogenními regresory, abychom vyhodnotili fluktuace politicky neutrální sazby v čase. Nalézáme, že politicky neutrální sazba v čase klesá na úroveň srovnatelnou se zeměmi eurozóny. Dále navrhujeme způsob měření nastavení měnové politiky založeném na rozdílu mezi skutečnou úrokovou mírou a námi odhadnutou politicky neutrální sazbou a nalézáme, že tímto způsobem jsme schopni dobře predikovat budoucí inflaci i budoucí změnu inflace. Klíčová slova politicky neutrální úroková míra, Taylorovo pravidlo, model s časově proměnlivými parametry a endogenními regresory Kontaktní adresa / Contact address Roman Horváth, M .A, Česká národní banka a Institut ekonomických studií, Karlova univerzita v Praze (e-mail: roman.horvath@gmail.com) Roman Horváth, M.A. Je absolventem Central European University. V současné dobé pracuje jako starší ekonom odboru ekonomického výzkumu a finanční stability v České národní bance. 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Princeton University Press, Princeton: New Jersey. Internet resources: CNB - The Monetary Policy of the Czech National Bank, http://www.cnb.cz/www.cnb.cz/en/about_cnb/missions_and_functions/mp_faktsheet_ en.html APPENDIX Table A.I - KPSSTest Series Test statistic PRIBOR3M 0.355* CPI Inflation 0.165 I CPI Inflation forecast (t+12) 0.163 Net Inflation 0.147 Output gap - HP filtered 0.106 Output gap - Real-time 0.293 I Output gap - Ex-post 0.214 M2 growth 0.168 Real effective exchange rate 0.447* The null hypothesis is that the series is level stationary. Critical values for the null hypothesis: 10% - 0.347, 5% - 0.463, 1%- 0.739. Sample period: 2001:1-2006:09. * ** *** denotes significance at the 10,5 and I percent level, respectively. ACTA VSFS, 1/2008, roc. 2 099 Chart A.I - Interest Rate, Output Gap and Inflation Note: This chart presents current inflation, short-term interbank interest rate (3M PRIBOR) and CNB output gap as of October 2006 forecast round. Chart A.2 - Comparison of Output Gap Estimates 2001 2002 2003 2004 2005 2006 —'- Gap - ex post —*— Gap - real-time —"- Gap - HP filter Note: This chart presents three measures of output gap used in the paper: Output gap estimated by the CNB as of their October 2006 forecast round (Gap - ex post), Real-time based output gap estimated by the CNB (Gap - real-time) and the output gap calculated using HP filter (Gap - HP filter) as the estimate of potential output. 100 ACTA VSFS, 1/2008, roc. 2 Table A.2 - Monetary Policy Rules Estimation rt={\ -p) r )+ßx, + pr,_x + £ rt = r,-\ + #„ 0t ~ i.i.d.N(o,al) e, = Kv,e(Te,tvt+K9,e i, ~ Mo,(i-<£ ) Model : Parameters l 2 3 4 5 6:7 s 9 10 11 12 P 0.40"' : 0.40*** 0.40*** 0.41*** 0.40*** : 0.40*"" : 0.42*** 0.40*** ■■ QA2„, 0.42*** 0.45*** 0.40"' (0.02) : (0.09) (0.06) (0.06) (0.07) : (0.09) : (0.11) (0.10) ■■ (0.10) (0.09) (0.10) (0.15) a 0.27™ 0.07 0.28*** 0.06 0.28*** 0.07 ' -0.15 -0.15 -0.18 -0.16 -0.17 -0.14 (0.07) (0.07) (0.08) (0.06) (0.07) ' (0.06) ' (0.12) (0.11) i (0.11) (0.11) (0.10) (0.09) ß 0.21 0.11 -0.06 0.57" -0.06 -0.06 ' 0.12 0.14 ' 0.66" 0.66" 0.18 -0.02 (0.24) (0.24) (0.28) (0.29) (0.22) ' (0.23) ' (0.27) (0.25) ' (0.28) (0.31) (0.23) (0.19) K'v., -0.06"* ' -0.07*** -0.06" \ \ 0.01 0.02 0.02 (0.01) ; (0.02) (0.02) ! (0.01) : (0.01) (0.01) -0.02* -0.02* -0.02* ! 0.01 -0.01 -0.02*** (0.01) ; (0.01) (0.01) i (0.01) (0.02) (0.01) AIC -1.10 -1.00 -1.07 -1.00 -0.95 -0.94 . -0.91 -0.94 -0.94 -0.96 -0.91 -0.88 Note: Robust standard errors in brackets. ***, ** and *indicates the significance at 1,5 and 10%, respectively. Models differ according to whether bias correction terms are included and the specification of ^",+, and xt. ftt+i is eitherCNB inflation forecast one year ahead (abbreviated as IF below) or current inflation rate (IC). xt is a measure of output gap: 1. as estimated by HP filtering (HP), 2. CNB ex-post output gap measure based on multivariate Kalman filter procedure (EX), 3. CNB real-time output gap measure based on multivariate Kalman filter procedure (REAL). Model 1and2 = IC, HP; Model 3 and 4 = IC, EX; Model 5 and 6 = IC, REAL; Model 7 and 8 = IF, HP; Model 9 and 10 = IF, EX and Model 11 and 12 = IF, REAL; ACTA VSFS, 1/2008, roc. 2 101 Chart A.3 - Importance of Bias Correction Terms in Estimating Policy Rules Backward-looking policy rule 2001 2002 2003 2004 2005 2006 \ \ lift w vis V 2001 2002 2003 2004 2005 2006 2001 2002 2003 2004 2005 2006 Current inflation, output gap - HP filter Current inflation, output gap - ex-post Forward-looking policy rule Current inflation, output gap - real-time > < 1/5 A ^ \ • V A - —^ wv—' — i if/ **y r v WV >--=— /"\ w—^~~v— ■•v 1 Jl Ml -'WV--- ■U If i 2001 2002 2003 2004 2005 2006 2001 2002 2003 2004 2005 2006 2001 2002 2003 2004 2005 2006 nflation forecast - real-time, output gap - HP filter ! Inflation forecast - real-time, output gap - ex-post ! Inflation forecast - real-time, output gap - real-time Note chart A3: The difference between the policy neutral rates estimated from the time-varying parameter model with endogenous regressors, rt,e with its confidence intervals, and from the conventional time-varying parameter model, r t,c. The measure of output gap and inflation is used for estimation of policy neutral rate is reported below each chart. Consequently, if the confidence intervals are different from zero, it means that r,,c does not lie within the confidence intervals of rt.B . Table A.3 - Monetary Stance and Future Level of Inflation (I \ /_ \ rt - r, A' j / ) \ i Adj. R2 12 \ 1.43*** \ -6.89 \ 0.07 13 \ 1.31*** i -9.91* \ 0.15 14 \ 1.26*** \ -11.30** \ 0.19 15 i i 26*** | -11.58** | 0.20 16 \ 1.22*** \ -13.23** \ 0.27 17 \ 1.20*** \ -14.31*** \ 0.32 18 \ 1.23*** \ -13.93*** \ 0.31 19 i 1.14*** \ -16.02*** \ 0.39 20 \ 1.18*** \ -15.81*** \ 0.39 21 \ 1.25*** \ -14.81*** \ 0.36 22 \ 1.31*** \ -13.82** \ 0.32 23 ; i _42*** \ -12.54** \ 0.30 24 \ 1.57*** i -10.16* 0.21 Note: Robust standard errors. ***, ** and ^indicates the significance at 1,5 and 10%, respectively. ACTA VSFS, 1/2008, roc. 2 103 Table A.4 - Monetary Stance and Future Level of Inflation, Controlling for Lagged Inflation ff = i rt vv h=\ -h +V,H : / 0O 0 0, 0, 0: 0s ! Adj. R2 ! 12 \ 2.33*** \ -0.94 0.03 0.04 \ 0.07 \ -0.48 i 0.33 13 \ 1.95** i -2.49 -0.11 0.19 i -0.06 i -0.33 i 0.41 14 \ 1.67* i -3.59 -0.14 0.04 i 0.19 i -0.36 i 0.46 15 | 1.49 | -4.26 -0.25 0.24 | -0.07 | -0.15 | 0.48 16 \ 0.66 \ -6.86** -0.09 -0.07 \ -0.22 \ 0.30 \ 0.52 17 \ 0.02 I -8.89*** -0.25 -0.16 \ 0.14 \ 0.31 \ 0.57 18 \ -0.33 I -9.98*** -0.55*** 0.19 \ 0.14 \ 0.33 ; o.60 19 ; -1.05 \ -12.12*** -0.57*** 0.20 \ 0.27 \ 0.36 \ 0.63 20 \ -1.12 \ -12.27*** -0.62** 0.36 \ 0.17 \ 0.38 ; o.60 21 j -0.78 \ -11.09** -0.46 0.18 \ 0.21 \ 0.34 | 0.51 22 j -0.57 \ -10.31** -0.42** 0.25 \ -0.09 \ 0.52 \ 0.45 23 i -0.48 i -9.86** -0.26 -0.06 i 0.01 i 0.61* i 0.41 24 i -0.53 i -9.89** -0.40 0.12 i -0.12 \ 0.73* . 0.39 Note: Robust standard errors. ***, ** and indicates the significance at 1,5 and 10%, respectively. 104 ACTA VSFS, 1/2008, roc. 2 Table A.5 - Monetary Stance and Future Change of Inflation Km -Kt=A+x rt - r, r, + Vt. i 0o 0, Adj. R2 12 i -3.04*** \ -15.39*** \ 0.53 13 \ -3.29*** \ -16.55*** \ 0.57 14 i -3.48*** \ -17.47*** \ 0.59 15 j -3.54*** J -17.77*** J 0.59 16 \ -3.58*** \ -18.01*** \ 0.60 17 \ -3.60*** \ -18.09*** \ 0.60 18 \ -3.56*** \ -17.93*** \ 0.59 19 \ -3.60*** \ -18.05*** \ 0.60 20 \ -3.54*** \ -17.81*** \ 0.60 21 \ -3.42*** \ -17.24*** \ 0.60 22 \ -3.28*** \ -16.62*** \ 0.58 23 i -3.10*** \ -15.88*** i 0.56 24 \ -2.89*** \ -15.11*** 0.53 Note: Robust standard errors. (and ^indicates the significance at 1,5 and 10%, respectively. ACTA VSFS, 1/2008, roc. 2 105 Table A.6 - Monetary Stance and Future Change of Inflation, Controlling for Lagged Inflation -n,=0o+0i {jj< ~ r< r< j + 2 0*+!*«-* : Z 0o 02 I 03 04 I 0s Adj. R2 12 \ 2.12*** \ -1.26 -1.11*** i -0.08 \ 0.53* i -0.59 \ 0.82 13 j 1.62* \ -3.18 -1.26*** i 0.05 i 0.43 i -0.42 i 0.84 14 i 1.41 i -4.06 -1.28*** i -0.11 i 0.67* i -0.46 \ 0.85 15 i 1.44 \ -4.10 -1.41 *** i 0.08 i 0.46 i -0.33 \ 0.86 16 i 0.56 \ -6.82* -1.24*** i -0.23 i 0.33 i 0.13 \ 0.86 17 i -0.08 i -8.89** -1.41 *** i -0.31 i 0.69** i 0.14 \ 0.89 18 i -0.33 ! -9.70*** -1.72*** i 0.05 i 0.68* i 0.14 \ 0.89 19 i -1.13 \ -12.05*** -1.74*** i 0.07 i 0.80** i 0.19 \ 0.88 20 i -1.19 \ -12.20*** -1.79*** i 0.23 i 0.70* i 0.20 \ 0.87 21 i -0.86 \ -11.03*** -1.63*** i 0.02 \ 0.77* i 0.16 \ 0.86 22 i -0.67 \ -10.31*** -1.61*** i 0.12 i 0.45 i 0.36 \ 0.85 23 i -0.49 ! -9.55*** -1.45*** i -0.13 i 0.42 i 0.48* \ 0.85 24 J -0.51 ' _9 49*** -1.57*** J 0.02 J 0.32 J 0.59** J 0.86 Note: Robust standard errors. ***, ** and indicates the significance at 1,5 and 7 0%, respectively. 106 ACTA VSFS, 1/2008, roc. 2